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Pathology of Traveling-Salesman Subtour-Elimination Algorithms

Author

Listed:
  • Mandell Bellmore

    (The Johns Hopkins University, Baltimore, Maryland)

  • John C. Malone

    (McKinsey and Company, New York, New York)

Abstract

The traveling-salesman problem has been the target of a substantial number of computational algorithms over the last two decades. Reported computational experience with these algorithms varies widely; authors, however, have generally failed to explain this variation adequately, or to offer predictive theories for their approaches. This paper (a) develops an underlying theory for the problem, (b) predicts pathological performance of some existing techniques, and (c) presents two algorithms, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.

Suggested Citation

  • Mandell Bellmore & John C. Malone, 1971. "Pathology of Traveling-Salesman Subtour-Elimination Algorithms," Operations Research, INFORMS, vol. 19(2), pages 278-307, April.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:2:p:278-307
    DOI: 10.1287/opre.19.2.278
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    Cited by:

    1. Belhoul, Lyes, 2014. "Résolution de problèmes d'optimisation combinatoire mono et multi-objectifs par énumération ordonnée," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14672 edited by Vanderpooten, Daniel.
    2. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    3. Nait Tahar, Djamel & Yalaoui, Farouk & Chu, Chengbin & Amodeo, Lionel, 2006. "A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 63-73, February.
    4. Lysgaard, Jens, 1999. "Cluster based branching for the asymmetric traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 119(2), pages 314-325, December.
    5. Carter, Arthur E. & Ragsdale, Cliff T., 2006. "A new approach to solving the multiple traveling salesperson problem using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 175(1), pages 246-257, November.
    6. M Blais & G Laporte, 2003. "Exact solution of the generalized routing problem through graph transformations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 906-910, August.

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